When client browsers connect to a SSL server, they check that the server name (as specified in the URL) is part of the name(s) which are present in the certificate. Exact rules are given in all their technical glory in RFC 2818, section 3.1.
For your situation, sharing the certificate between the two servers will work if they both share the same DNS name (but this may prove difficult, since they are likely to have distinct IP addresses), or if you convince your certificate issuer to give you a certificate with both server names in it (since the business model of most commercial CA relies on selling as many certificates as possible, they may object to selling you a single certificate instead of two).
One additional point is that private keys ought to travel as least as possible. If both servers share the same certificate, then they know the same private key, so the private key must have traveled quite a bit (at least from UK to South Africa, or the opposite). This can be done relatively safely (e.g. through some SSH connection) but, on a general basis, this is not recommended.